Abstract
Recently it is found that, due to Weyl anomaly, an external magnetic field can induce anomalous currents near a boundary. In this note, we study anomalous currents for complex scalars and Dirac fields in general dimensions. We develop a perturbation method to calculate Green's function in the spacetime with boundaries. By applying this method, we obtain anomalous currents up to the linear order of magnetic fields in a half space and in a strip. To the best of our knowledge, the results for Dirac fermions and for strips are new. It is remarkable that, unlike the scalars and holographic BCFT, the anomalous currents of Dirac fields are independent of boundary conditions in general dimensions. Besides, the currents of Dirac fields are always larger than those of complex scalars. Finally, we find an exact formal expression of the anomalous current in a half space. The result is expressed in momentum integrals, which can be evaluated numerically. We find that the mass suppresses the anomalous currents as expected.
Highlights
The anomaly-induced transport is an important phenomenon, which has a wide range of applications [1]
The well-known examples include chiral magnetic effect (CME) [2,3,4,5,6] and chiral vortical effect (CVE) [7,8,9,10,11,12,13], which refer to the generation of currents due to an external magnetic field and the rotational motion in the charged fluid, respectively
By applying Green’s function method, we derive the anomalous currents for free theories up to the linear order of external magnetic field in a half space and in a strip
Summary
The anomaly-induced transport is an important phenomenon, which has a wide range of applications [1]. The previous works [17,18] mainly discuss the general characteristics of anomalous currents They focus on the region close to the boundary. By applying Green’s function method, we derive the anomalous currents for free theories up to the linear order of external magnetic field in a half space and in a strip. We obtain an exact formal expression of the anomalous current for complex scalars in a half space. (1) Unlike the holographic BCFT [18] and complex scalars, the anomalous currents of Dirac fields are independent of BCs in general dimensions. We use conventions of [61] and the signature of metric is ð1; −1; ...; −1Þ
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